Evidence for Ferroelectricity in Iv-Vi Compounds G

EVIDENCE FOR FERROELECTRICITY IN IV-VI COMPOUNDS G. Pawley

To cite this version:

G. Pawley. EVIDENCE FOR FERROELECTRICITY IN IV-VI COMPOUNDS. Journal de Physique Colloques, 1968, 29 (C4), pp.C4-145-C4-150. 10.1051/jphyscol:1968423. jpa-00213627

HAL Id: jpa-00213627 https://hal.archives-ouvertes.fr/jpa-00213627 Submitted on 1 Jan 1968

HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE Colloque C 4, supplkment au no 11-12, Tome 29, Novembre-Dkcembre 1968, page C 4 - 145

EVIDENCE FOR FERROELECTRICITY IN IV-VI COMPOUNDS

Department of Natural Philosophy - The University, Edinburgh, Scotland

Rbum6. - Parce que les mkthodes habituelles servant h ktablir le caractkre ferroklectrique des cristaux ne sont pas applicables au cas de corps de haute conductivitk, on doit alors introduire d'autres moyens basks sur d'autres propriktks ferroklectriques. L'analyse de la structure cristalline peut fournir un modile montrant la possibilitk de polarisation reversible, mais une preuve plus convaincante peut venir de l'ktude de la dynamique du cristal. La diffusion inklastique cohbente des neutrons donne les frkquences des modes normaux du cristal et la variation en tempkrature de certains modes peut indiquer la ferroklectricite ou I'antiferrokkctricite. Des exemples de ces ph6- nomines sont prksentts pour SnTe, suggkrant, de plus, que les solutions solides de SnTe avec GeTe forment un vaste domaine oh existe le caract6re ferroklectrique. Abstract. - Because the usual methods for establishing ferroelectricity in crystals are not possible for crystals with high conductivities, other ways must be introduced based on other ferroelectric prop&rties. ~nalysisofthe crystal structure can provide a model showing the possibility of reversible polarisation, but more convincing evidence can come from the study of the dynamics of the crystal. Neutron inelastic coherent scattering yields the frequencies of the normal modes of the crystal, and the temperature dependence of certain modes can point to ferroelectricity or antiferroelectricity. Examples of both these phenomena are presented for SnTe, suggesting moreover that the solid solutions of SnTe with GeTe form a wide ferroelectric range.

1. Introduction. - The standard methods of could be classed as ferroelectric. We wish to extend establishing the existence of ferroeIectricity in a the classification so as to include those semi- crystalline substance have until recently been sufficient conducting (or even metallic) crystals which display to remove any doubt in most cases [I]. Ferroelectricity other properties indicative of ferroelectricity. Here is confirmed by hysteresis in the E-D (field- we turn to Cochran's [2] theory of ferroelectricity displacement) relationship. The crystal is polarised and show, with SrTiO, as an example, the permanently in a certain direction, but this polarisation relationship between the dielectric phenomena and can be reversed by application of a large enough field, the variation of a certain mode of vibration of the known as the coercive field. The resulting crystal crystal. structure (at least for any case of interest here) is A basic relation between certain modes of vibration related to the initial structure by centrosymmetric of a crystal and its dielectric constants has been proved inversion. Clearly this means that the ferroelectric by Lyddane, Sachs and Teller 131. crystal structure must be acentric. The ferroelectric transition occurs between this acentric structure and a centric structure, that is from the ferroelectric to the paraelectric phase. Evidence for the onset of ferroelectricity can be found in the paraelectric phase Here V~.~.(O)and v,.,.(O) are the frequencies of the by studying the temperature variation of the static longitudinal and transverse optic modes with zero dielectric constant, ~(0).This follows a Curie-Weiss law wave number, ~(0)and ~(co)are the static and high frequency dielectric constants. Cochran and Cowley [4] have shown that, for a structure with n optic modes

Conventional evidence for ferroelectricity clearly depends on the crystal being an insulator. No crystal with substantial conductivity could show any of the Cochran [27 argues that the lowest frequency transverse dielectric phenomena above, therefore no such crystal optic (T. 0.)mode is highly temperature dependent

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1968423 C 4 - 146 G. S. PAWLEY while all the other modes are relatively constant. Thus if the Curie-Weiss law, equation (I), is obeyed, this T. 0. frequency varies as

Strontium titanate has a Curie temperature of 32 OK, and we are here interested in the phenomena in the cubic paraelectric phase. The exact nature of the transition or transitions is however still uncertain. The temperature dependence of the lowest T. 0. mode has been measured by Cowley [5] using the technique of neutron inelastic scattering and his measurements of the dispersion relation for the phonon branch with wave vectors along [loo] are shown in figure 1.

FIG.2. -The temperature variation of the reciprocal of the static dielectric constant and the square of the frequency of the transverse optic mode of zero wave number for SrTiOs.

crystal, containing only five atoms in the unit cell. Cochran [7] in studying PbTe, pointed out that there is in principle no reason why a diatomic ionic crystal should not have a ferroelectric transition Work on PbS and PbTe [8], both n-type extrinsic semiconductors with carrier concentrations of about 10'' crnF3, led to the study of SnTe, a p-type semiconductor with a much higher carrier concen- tration. All these substances have the NaCl structure, so it is instructive to compare their phonoa dispersion curves with those of KBr and NaI [9]. Figure 3 shows part of the measured dispersion curves for these Reduced wove vector 3 2z five crystals. This part, similar in each case, is sufficient FIG. 1. -The dispersion in the lowest transverse optic for our present purposes. Figure 3 (a) and (b) show branch of SrTiO3 for wave vectors along [loo] at 90 OK and KBr and NaI in which we see that the T. 0. branch 296 OK. THz a This contains results at two temperatures whereas 7 - figure 2 shows values of V;~(O)at a number of temperatures. Figure 2 also shows the variation of E(o)-' with temperature, as measured by Mitsui and Westphal [6], and the juxtaposition of these results 3- emphasies the simultaneous validity of equations (1) 2- and (4). Thus the appropriate temperature variation 1 - of the dielectric constant or the frequency of the n-- lowest T. 0.mode (the ferroelectric, soft or Cochran - - - - - mode) are equivalent evidence for a ferroelectric IReduced wave vector +om the origin to the zone boundary transition. FIG. 3. -The measured phonon dispersion curves for five crystals with the NaCl structure for wave vectors along [loo]. 2. Diatomic ferroelectrics. - For some years (a) KBr at 90 OK, (b) NaI at 100 OK, (c) PbS at 296 OK, (d) PbTe BaTi03 has been the simplest known ferroelectric at 296 OK, (e) SnTe at 100 OK. EVIDENCE FOR FERROELECTRICITY IN IV-VI COMPOUNDS C4- 147 is flat in both cases. In contrast the T. 0. branches measurements would not quite become unstable for PbS, PbTe and SnTe (Fig. 3 (c), (d) and (e)) show against the T. 0. mode of vibration at absolute zero. a marked drop as the wave vector tends to zero. This The phonon dispersion curve measurements are effect is most noticeable in SnTe and prompted ideal for use in the study of models for the forces in measurements at a number of temperatures [lo]. crystals, and the (( shell )) model has proved most The results are shown in figures 4 and 5 respectively. useful for ionic crystals 18, 93. This model is an extension of Born's model, taking into account the electronic polarisability of the ions. This model has provided a good fit with experiment for KBr and NaI but a progressively poorer fit for PbS, PbTe and SnTe. The effect of screening by the carriers in the last three crystals is seen (Fig. 3) in the drop in the longitudinal optic (L. 0.) branch frequency when the wave number is of the order of or less than the Thomas-Fermi screening length [8]. An attempt to modify the shell model to take account of the effect of screening on all the dispersioil branches has met with some success [I 11. 3. The a-GeTe transition. - It has been established that GeTe undergoes a phase transition, thought to be second order, from a cubic phase with the NaCl structure above 670OK to a rhombohedra1 phase below this temperature [12]. The lower symmetry structure is known as a-GeTe. In addition GeTe and SnTe form a continuous range of solid solutions, and at each FIG. 4. -The dispersion3f the optic modes of vibration colnposition there is a definite transition temperature with wave vectors along [I001 in SnTe at various temperatures. which varies almost linearly with composition. Extra- polation to pure SnTe gives a transition temperature about 0 OK which is not inconsistent with the lattice dynamical evidence. Arguing from the phonon dispersion curve measurements we could have predicted the crystal structure of a-GeTe. In a mode of vibration at zero wave number all the atoms of one chemical species are moving in unison, and for the optic mode both species are moving in opposition. Figure 6 shows how the amplitude of this mode of vibration in the NaCl structure on

1 I I I1 0 100 200 300 TEMPERATURE FIG. 5. - The square of the transverse optic mode frequency at zero wave number as a function of temperature, in SnTe. FIG. 6. -The ferroelectric mode in the GeTe transition. The obvious similarity provides lattice dynamical At Ieft is the primitive rhombohedron of the NaCI type structure, evidence of an approach to a ferroelectric phase, and at right the structure of the lower phase with displacements suggesting that the crystal of SnTe used for these exaggerated. a Te, o Ge. C 4 - 148 G. S. PAWLEY the left increases as the temperature is lowered towards do not rely on X-ray intensities but on more accurately the transition temperature. measurable lattice parameters. They point out the The amplitude increases as the frequency falls until most interesting result that the observed phase transi- the crystal becomes unstable and transforms to the tion is similar to the transition of antimony to a cubic rhombohedral structure on the right. The central atom in this diagram is evidently germanium as its displacement would be greater than that of tellurium in this mode as germanium is the lighter atom. The germanium atom is positioned on the main body diagonal of the rhombohedron distant u f 0.5 frac- tional units from the tellurium. Evidently both u and (1 - u) are equally probable, corresponding to the two ferroelectric structures. Much therefore depends on the results of X-ray structure analysis. This has received much recent atten- FIG.7. -Electron density along the main'diagonal of the tion [13, 14, 151 with conflicting conclusions. Goldak et rhombohedral GeTe unit cell, showing the acentric positioning al. [13] present the most accurate set of results, namely of the atoms 1141. counter measurements of ten reflections from a powder specimen (no work has yet been reported on single phase at 70 kbar. Indeed the similarities between the crystals). They fit the distorted acentric structure by Group V elements and the IV-VI compounds have least squares and obtain a high reliability factor, been appreciated for some time. It was in fact just this similarity which prompted the band structure work of Cohen, Falicov and Colin [16] who predicted the acentric a-GeTe structure, leading on to the where I,,, and I,,,, are the observed and calculated structure analysis 1131. X-ray intensities. They find difficulty with the tempe- Having dispersed all doubt about the cc-GeTe struc- rature factors and present an unrealistic model where ture we can now conjecture as to the structure of the temperature factor for the heavier atom is higher Pb, (TI, Bi)l-,- S . than for the lighter atom. However they show that a 2 large variation in temperature factors does not alter their estimate for u of .474 + .004. No account is This has been shown [17], again by studying cell dimen- taken of the known slight deficiency of germanium in sions, to have a cubic phase and a rhombohedral the crystal structure, but their results could not possi- phase. Figure 8 indicates the point in the solid solution bly be explained in terms of a centrosymmetric model. range where the transition occurs. The usefulness of This result is supported by Zhukova & Zaslavskii [14]. IV-VI compounds as piezoelectric semiconductors has They give more results than [13], again counter measurements, and find u = 0.47 (no error given) by a trial and error procedure. The R factor, calculated for the present article using the same 10 reflections of [13] was 0.17. This is dominated by one poor agree- ment, otherwise the comparison with [3] is very good. They conclude by giving u = 0.466, obtained by a Fourier summation shown in figure 7. Kabalkina et al. [15] are concerned mainly with the transition to the cubic structure at 40 kbar, which they show is probably first order. Here no X-ray intensities are given, but it is concluded that u = 0.50. One set of intensities is given at a different pressure and are so approximate that no conclusion about the crystal structure could be based on them. We must disregard this result and accept that the structure is indeed acentric, as in figure 6. FIG. 8. - Variation of the cell parameters with composition of Pbz (TI, Bi) 1-1 S after Malevskii [17]. The other results which Kabalkina et al. [15] obtain (7) EVIDENCE FOR FERROELECTRICITY IN IV-VI COMPOUNDS C4- 149 been hampered by high conductivity, but as theconduc- tivity of PbS can be considerably reduced this system has promise of applications. One application has been suggested by Gulyaev and Karabanov [la] where a layered piezoelectric and semiconductor is required. With the modern method of doping at specific depths by bombardment this suggestion could certainly be realised. 4. Antiferroelectricity. - SnTe undergoes another type of phase transition not mentioned before in this paper. At high pressures (1 8 kbar [19]) the cubic phase gives way to an orthorhombic phase where the structure is similar to that of SnS and SnSe (see Wykoff [20]). The cell dimensions are roughly 2 a : a/& : a/& where a is the lattice parameter for the NaCl type cube. Scrutiny of the structure suggests a mechanism for this transition. Although the rigour of group theory FIG. 10. -The symmetry of figure 9 as viewed down z, could be applied a diagrammatic explanation gives a and the subgroup symmetry of the SnS structure. deeper understanding [21]. Figure 9 shows part of an NaCl type structure with the 2 a : a/fi : a/JZ cell outlined. Looking down the z-axis at this cell we see the structure and symmetry of

FIG. 9. -Part of an NaC1-type structure with an orthorhombic cell outlined. figure 10 (a). Below this in figure 10 (b) is the symmetry FIG. 11. - The SnS structure, suggesting wave-like displa- of the SnS structure (Pbnm) which is evidently a sub- cements from an NaC1-type structure. group of figure 10 (a). Figure 11 shows arrows from the undisturbed NaCl positions to the known positions direction. This corresponds to a point on the right in SnS, suggesting a wave of displacements within the hand side of the dispersion curves of figure 3. We crystal. The wave drawn in figure I1 cuts the arrows would therefore expect to see the frequency in the to the sulphur positions because in any mode of lowest branch at this point decrease as pressure is vibration of this sort the lighter atoms are displaced applied to the crystal. Alternatively at one pressure more than the heavier atoms. The wavelength of this we would expect the frequency in the branch to drop as wave is clearly 2 a, the atomic displacements are trans- the wave vector tends to the zone boundary. This lat- verse and the variation takes place along the [loo] ter effect is noticeable only in SnTe, and although the direction. Consequently this wave is the transverse effect is small the measurements are accurate enough zone boundary mode with wave vector in the [loo] for the drop to be significant. C4- 150 G. S. PAWLEY

It is clear that the SnS structure classes as antiferro- References electric as the polarisation in one half of the unit cell [l] JONA(F.) and SHIRANE(G.), Ferroelectric Crystals. is exactly compensated by that in the other half. It Oxford : Pergamon, 1962. is not unrealistic to suggest therefore that the pressure [2] COCHRAN(W.), Advances in Physics, 1960, 9, 387. induced phase transition observed in SnTe [I91 is [3] LYDDANE(R. H.), SACHS(R. G.) and TELLER(E.), Phys. Rev., 1951, 59, 673. antiferroelectric, brought about by the instability [4] COCHRAN(W.) and COWLEY(R. A.), J. Phys. Chem. of the crystal against a mode of vibration (Fig. 12) in Solids, 1962, 23, 447. accordance with Cochran's theory as extended to [5] COWLEY(R. A.), Phys Rev., 1964, 134, A981. antiferroelectricity [22]. [6] MITSUI(T.) and WESTPHAL(W. B.), Phys. Rev., 1961, 124, 1354. [7] COCHRAN(W.), Physics Letters, 1964, 03, 193. [8] COCHRAN(W.), COWLEY(R. A.), DOLLING(G.) and ELCOMBE(M. M.), Proc. Roy. Soc. (London), 1966, A293, 433. [9] WOODS(A. D. B.), BROCKHOUSE(B. N.), COWLEY (R. A.) and COCHRAN(W.), Phys. Rev., 1963, 131, 1025. [lo] PAWLEY(G. S.), COCHRAN(W.), COWLEY(R. A) and DOLL~NG(G.), Phys. Rev. Letters, 1966, 17, 753. [ll] COWLEY(E. R.), DARBY(J. K.) and PAWLEY(G. S.), in preparation. FIG. 12. -The SnTe antiferroelectric mode of vibration. [12] BIERLY(J. N.), MULDAWER(L.) and BECKMAN(O.), Acta Met., 1963, 11, 447. It might be argued that the displacements in SnS 1131 GOLDAK(J.), BARRETT(C. S.), INNES(D.) and YOUDELIS(W.), J. Chem. Phys., 1966, 44, 3323. from which the above deductions are made are much [14] ZHUKOVA(T. B.) and ZASLAVSKII(A. I.), Kristallo- too large to constitute a << frozen mode x ; too large, grafya, 1967, 12, 37. in other words, to be the amplitude of the mode of [IS] KABALKINA (S. S.), VERESHCHAGIN(L. F.) and vibration at the time of transition. However SnS SEREBRYANAYA(N. R.), Z. Exp. Theor. Fiz., 1966, 51, 1358. itself is not known to have a NaCl type structure or a [16] COHEN(M. H.), FAL~KOV(L. M.) and Go~m(S.), phase transition. Its orthorhombic structure must be I. B. M. Jour. Res. Develop., 1964, 8, 215. much more stable than that of SnTe so we might [17] MALEVSKII(A. Yu.), Doklady, 1966, 169, 1324. expect the displacements from SnS to be an exaggera- 1181 GULYAEV(Yu. V.) and URABANOV(A. Yu.), Fiz. Tech. Polziprovodnikov, 1967, 1, 753. tion of the (< frozen mode )) in SnTe. 1191 KAFALAS(J. A.) and MARIANO(A. N.), Science, 1964, 143, 952. 5. ConcIusion. - Evidence for ferroelectricity need [20] WYCKOFF(R. W. G.), Crystal structures, Vol 1. not rest on electrical measurements. Analysis of the New York : Wiley, 1963. crystal structures both above and below the phase [21] C~CHRAN(W.) and ZIA (A.), Phys. Stat. Sol., 1968, transition can suggest a mode of vibration which plays 25, 273. [22] COCHRAN(W.), Advances in Physics, 1961, 10, 401. an important part in the phase transition. As the crystal in the high symmetry phase is brought in tempera- BIRMAN, J. - Your conjecture about possible ture towards the transition, the frequency of this mode instability of a zone edge mode showing the SnS struc- drops until the amplitude is large enough to cause ture as a c( distorted rocksalt, antiferroelectric >> transition. The ultimate test of this mechanism of may receive some indirect support from the recent, transition is to measure the frequency of this mode as similar, proposal by P. A. Fleury, J. F. Scott and a function of temperature, which is done most ele- J. N. Worlock (Physical Review Letters, 21, 16, 1968) gantly by neutron inelastic coherent scattering. relating to the interpretation of the 110 OK phase transition in SnTiO, as involving zone edge mode Acknowledgements. - I wish to thank all those instability. with whom 1 have been associated in the work on SnTe [10,1I], and the Atomic Energy of Canada Ltd., PAWLEY,G. S. - We hope that this is so, and this whose equipment was used for the SnTe measure- transition is already under study at Chalk River, using ments. the crystal of reference [5].